My camera does these things too, apart from the af issue you're having.

Start up can often take an age before it lets me take a picture, waiting for the info to appear takes the longest part of this time. I have observed the shutter sound, like taking a pic or two on shut down that you have mentioned. I haven't posted about it before as I guess I'm just quietly hoping a firmware update will fix it.

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Neil.

Hi Neil

Thanks for letting me know that you have heard the shutter firing on shut down I thought I was hearing things.

Firmware I have read several post on the Sony forums that Sony hardly ever update its firmware.